A mathematical model of the reverse-flow reactor for the catalytic conversion of methane to synthesis gas is presented. The model contains 8 partial differential equations and 6 algebraic equations. The analysis performed and the literature data suggest a considerable influence of the diffusional resistance in the catalyst pellet upon the actual rate of reactions occurring in the process. A simple approximate procedure is developed for the estimation of the effectiveness factor of the reactions, which enables the resistance due to internal diffusion to be taken into account at any point of the reactor without resorting to numerical integration of the diffusion equations in the pellet. A comparison is presented between the effectiveness factor eta obtained via the integration of the diffusion equations and that calculated using the linearized reaction rate equations. To solve the model of the whole reactor the software package PDEX1M is used which makes it possible to continuously adapt the temporal and spatial steps. The package adapts the local density of the grid in such a way that an assumed value of the error of computations can be obtained. Results of simulations for the reverse-flow reactor, carried out for eta varying in the reactor are compared with those done at an arbitrarily selected constant value of eta. A possibility of lowering the maximum temperature in the catalytic bed by altering the pellet size and adding H2O into the feed gas is analysed.